Measuring the Cosmic Ray Spectrum with Next Generation Neutrino Detectors

We investigate the capabilities of upcoming kiloton-scale neutrino detectors, such as Hyper-Kamiokande, in determining the primary cosmic ray spectrum. These detectors provide full-sky coverage and long-term monitoring, unlike traditional satellite and balloon experiments that measure cosmic ray flux at specific altitudes and locations. By analyzing the atmospheric neutrino flux generated by cosmic ray interactions, we demonstrate that future detectors can differentiate between various cosmic ray models with high statistical significance, even when accounting for uncertainties in neutrino cross sections and hadronic interactions. We introduce a technique for reconstructing the primary cosmic ray spectrum using neutrino measurements, which reduces the flux uncertainty from approximately 20\% to about 7\%. We then show that Hyper-K has the potential to increase sensitivity to neutrino oscillation parameters, such as $\sin^2\theta_{23}$, by a factor of 2. Our results highlight the complementary role of neutrino detectors in cosmic ray physics and their critical importance for precision measurements in particle astrophysics.